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Sinn Fein is opposed to the next Northern Ireland police chief being appointed from within the organisation, Mary Lou McDonald has indicated.
The party president said she did not have confidence in any of the current senior PSNI command team to succeed George Hamilton after he retires in June.
Mrs McDonald said the PSNI had "zero credibility" in its handling of cases linked to the legacy of the Troubles.
Her comments came after she met bereaved families caught up in a controversy involving the police's failure to disclosure documents about historic killings to Northern Ireland's Police Ombudsman.
After the meeting in Belfast, Ms McDonald was asked if she had confidence in any of the current leadership team to replace Mr Hamilton.
"I don't," she replied.
The Sinn Fein leader added: "Is there somebody inside who I think should be the chief constable, and I have to answer honestly that no, I can't identify such a person.
"Lots of this is about who leads, who is in the top job in policing, but it goes much more broad than that. This is an issue of the culture of policing, it's about the systems and it's about their capacity to be and to be held fully accountable."
Last week, it emerged that the PSNI failed to disclose "significant information" relating to a notorious loyalist mass shooting.
Police Ombudsman Michael Maguire said "significant, sensitive information" around the incident at a bookmakers in south Belfast was not made available to his investigators.
Five people were killed on February 5 1992, when members of the Loyalist Ulster Freedom Fighters (UFF) opened fire on the Sean Graham bookmakers shop on the lower Ormeau Road.
Dr Maguire's office said the non-disclosed material, which it has now obtained, has opened new lines of inquiry in its investigation into the Ormeau Road shootings, as well as activities of loyalist paramilitaries in the north west between 1988 and 1994, and its probe into the murder of teenager Damien Walsh at a coal depot in west Belfast in 1993.
Last week, PSNI Deputy Chief Constable Stephen Martin apologised on behalf of the police and said they never sought to withhold the information from the ombudsman investigators, putting the incident down to human error.
Mrs McDonald, Sinn Fein vice president Michelle O'Neill and other party figures met a number of the impacted families at a community centre close to the scene of the Ormeau Road shootings on Monday afternoon.
The party members also met with police commanders earlier in the day.
Afterwards, Mrs McDonald was scathing in her assessment of the police.
"We have made absolutely clear to the PSNI that they have zero credibility in their dealing with legacy cases," she said.
"We have made it clear to the PSNI that their very cynical strategy and policy of withholding information or selectively disclosing some information and holding back the rest is entirely cynical, it's entirely unacceptable and it has dealt another blow to confidence in policing.
"But, more importantly, it has confirmed for very many families who have been waiting almost a lifetime in some cases, it has confirmed again that the policing authority in this state is not capable and not willing to act in an honourable, in a truthful and I would say in a fully democratic fashion when it comes to telling the truth."
However, Mrs McDonald's comments have caused widespread controversy, including amongst political parties here as well as the Police Federation for Northern Ireland (PFNI).
The PFNI called for an apology, saying the remarks were 'offensive' and an "extraordinary interference in an open and transparent selection process"
DUP MLA Mervyn Storey sits on the Policing Board and described the statement as 'outrageous'.
He added: "Policing Board members will be responsible for interviewing and assessing any future Chief Constable. How can any SF member sit on that panel and candidates from the PSNI expect to get a fair hearing? Anyone sitting on that panel must be fair and open-minded rather than having a pre-determined outcome.”
While Ulster Unionist Alan Chambers had this to say:
Alliance's John Blair added his criticism saying it was a 'careless and irresponsible thing to say'.